CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt171",{id:"formSmash:upper:j_idt171",widgetVar:"widget_formSmash_upper_j_idt171",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt173_j_idt175",{id:"formSmash:upper:j_idt173:j_idt175",widgetVar:"widget_formSmash_upper_j_idt173_j_idt175",target:"formSmash:upper:j_idt173:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operatorsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2007. , vii, 28 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 07:03
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-4344ISBN: 978-91-7178-626-5 (print)OAI: oai:DiVA.org:kth-4344DiVA: diva2:11908
##### Public defence

2007-05-09, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 09:00
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt481",{id:"formSmash:j_idt481",widgetVar:"widget_formSmash_j_idt481",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt487",{id:"formSmash:j_idt487",widgetVar:"widget_formSmash_j_idt487",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt493",{id:"formSmash:j_idt493",widgetVar:"widget_formSmash_j_idt493",multiple:true});
##### Note

QC 20100708Available from: 2007-04-25 Created: 2007-04-25 Last updated: 2010-07-08Bibliographically approved
##### List of papers

This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators.

In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator.

In Paper II we prove that the one-dimensional analog of this inequality holds even for the critical value of the moment parameter. In Paper III we establish Hardy-Lieb-Thirring inequalities for fractional powers of the Laplace operator and, in particular, relativistic Schrödinger operators. We do so by first establishing Hardy-Sobolev inequalities for such operators. We also allow for the inclu¬sion of magnetic fields.

As an application, in Paper IV we give a proof of stability of relativistic matter with magnetic fields up to the critical value of the nuclear charge.

In Paper V we derive inequalities for moments of the real part and the modulus of the eigen¬values of Schrödinger operators with complex-valued potentials.

1. On Lieb-Thirring inequalities for Schrödinger operators with virtual level$(function(){PrimeFaces.cw("OverlayPanel","overlay11903",{id:"formSmash:j_idt529:0:j_idt533",widgetVar:"overlay11903",target:"formSmash:j_idt529:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Lieb-Thirring inequalities on the half-line with critical exponent$(function(){PrimeFaces.cw("OverlayPanel","overlay11904",{id:"formSmash:j_idt529:1:j_idt533",widgetVar:"overlay11904",target:"formSmash:j_idt529:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators$(function(){PrimeFaces.cw("OverlayPanel","overlay11905",{id:"formSmash:j_idt529:2:j_idt533",widgetVar:"overlay11905",target:"formSmash:j_idt529:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value$(function(){PrimeFaces.cw("OverlayPanel","overlay11906",{id:"formSmash:j_idt529:3:j_idt533",widgetVar:"overlay11906",target:"formSmash:j_idt529:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials$(function(){PrimeFaces.cw("OverlayPanel","overlay11907",{id:"formSmash:j_idt529:4:j_idt533",widgetVar:"overlay11907",target:"formSmash:j_idt529:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1285",{id:"formSmash:j_idt1285",widgetVar:"widget_formSmash_j_idt1285",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1352",{id:"formSmash:lower:j_idt1352",widgetVar:"widget_formSmash_lower_j_idt1352",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1353_j_idt1355",{id:"formSmash:lower:j_idt1353:j_idt1355",widgetVar:"widget_formSmash_lower_j_idt1353_j_idt1355",target:"formSmash:lower:j_idt1353:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});